Question

4.11 q: a cardboard box of mass m on a wooden floor is represented by the free body diagram below. given the fbd, which of the following expressions could be accurate mathematical representations for the box? choose all that apply. (a) ( f_{n}-mg = ma_{x} ) (b) ( -f_{app}=ma_{x} ) (c) ( f_{n}-mg = ma_{y} ) (d) ( f_{app}=ma_{y} )

Explanation:

Step1: Analyze forces in x - direction

In the x - direction, the only force acting is \(F_{app}\) (assuming no other horizontal forces like friction shown explicitly in the FBD). Using Newton's second law \(F_{net,x}=ma_x\). The force \(F_{app}\) is in the negative x - direction. So, \(F_{net,x}=-F_{app}\), and \( - F_{app}=ma_x\)

Step2: Analyze forces in y - direction

In the y - direction, the normal force \(F_N\) acts upwards (+y) and the weight \(mg\) acts downwards (-y). Using Newton's second law \(F_{net,y}=ma_y\). So, \(F_{net,y}=F_N - mg\), and \(F_N - mg=ma_y\)

Answer:

B. \(-F_{app}=ma_x\), C. \(F_N - mg=ma_y\)